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2 years ago

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Mathematics

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mixas84 [53]2 years ago

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The inverse of matrix is (43, -11, 2).

<h3>What is inverse of matrix?</h3>

A matrix is a multidimensional generalization of the concept of reciprocal of a number: the product between a number and its reciprocal is equal to 1; the product between a square matrix and its inverse is equal to the identity matrix.

given equation:

x + 5y + 10z = 8

y + 4z = -3

x+6y + 15z = 7

The cofactors of the matrix is

C_11 = -9

C_12= 4

C_13=-1

C_21 = -15

C_22= 5

C_23 = -1

C_31= 10

C_32= -4

C_33= 1

The cofactor matrix is,

$\left[\begin{array}{ccc}-9 & 4 & -1\\-15 & 5 & -1\\10 & -4 & 1\end{array}\right]$

The transpose of matrix,

$\left[\begin{array}{ccc}-9 & -15 & 10\\4 & 5 & -4\\1 & -1 & 1\end{array}\right]$

The determinant of matrix is = 21.

The augmented matrix is attached below

Hence, the inverse of matrix is (43, -11, 2).

Learn more about this concept here:

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<h3>Law of syllogism</h3>

The law of syllogism, also known as transitivity reasoning, is a legitimate kind of deductive reasoning that adheres to a predetermined pattern. The transitive property of equality states that if a = b and b = c, then a = c. so we can conclude that The law of syllogism is almost similar to the transitive property.

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